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Home Data Science Data Science Tutorials Matlab Tutorial Matlab Unit Step Function
 

Matlab Unit Step Function

Updated March 6, 2023

Matlab Unit Step Function

 

 

Introduction to Matlab Unit Step Function

MATLAB unit step function is used to enable representation of a signal or pulse without the need to specify separate functional forms for various ranges of time. The unit step function is used to test the low and high-frequency response of any system in a single attempt. The unit step function takes theoretically zero time to change from 0 to 1. The unit step function is commonly called a Heaviside function.

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Syntax:

H = Heaviside (t)

Details of unit step or Heaviside function:

  1. H = heaviside (t) is used to evaluate the unit step function value at ‘t’
  2. It is discontinuous in nature and returns following values:
    1. 0 if t < 0
    2. 1/2 if t = 0
    3. 1 if t > 0

Let us now understand how to use a Heaviside function or unit step function in MATLAB. We will discuss the code to do the following:

  1. The use of the Heaviside function
  2. Plotting a Heaviside function

Please note that we will use a symbolic object as the input in the below examples. However, if we use a floating-point input, we will get a floating-point output. Since the output for t < 0 and t > 0 will be an integer, it will not make a difference. We can see the difference when input is t = 0 (refer to Example 3).

Examples of Matlab Unit Step Function

Let us discuss some examples of Matlab Unit Step Function:

Example #1

In this example, we will use the unit step function for input less than 1 and will see the output.

Code:

H = heaviside (sym (-10))

[Initializing the symbolic object and passing a negative number as an argument]

This is how our input and output will look like in MATLAB:

Input:

Matlab Unit Step Function example 1

Output:

Matlab Unit Step Function output 

As we can see, we have obtained 0 as the output for an argument which is a negative number, i.e. when ‘t’ is less than 0.

Example #2

In this example, we will use the unit step function for an input greater than zero.

Code:

H = heaviside (sym (20))

[Initializing the symbolic object and passing a positive number as an argument]

This is how our input and output will look like in MATLAB:

Input:

Matlab Unit Step Function ecample 2 input

Output:

Matlab Unit Step Function example output 2 

As we can see, we have obtained 1 as the output for an argument that is a positive number, i.e. when ‘t’ is greater than 0.

Example #3

This example will use the unit step function for an input greater than equal to zero. Here, we will discuss 2 scenarios:

  1. Using a symbolic object
  2. Not using a symbolic object (Using a floating-point input)

Code when using a symbolic object:

A = heaviside (sym (0))

[Initializing the symbolic object and passing zero as an argument]

This is how our input and output will look like in MATLAB:

Input:

Matlab Unit Step Function input

Output:

matlb 2

As we can see, we have obtained 1/2 as the output for an argument equal to zero.

 Code without using a symbolic object (Using floating-point input):

 H = heaviside (0)

[Passing zero as an argument to ‘heaviside’ function]

This is how our input and output will look like in MATLAB:

Input:

input

Output:

output

As we can see, we have obtained a floating-point when we have not used a symbolic object in the input.

Next, we will learn to plot the unit step function in MATLAB.

Example #4

In this example, we will plot the unit step function for values between 0 and 5. As we know, the unit step function gives 0.5 as output for t = 0 and 1 for t > 0, so for the values between 0 and 5, the output will be starting from 0.5 (for t = 0), and then it will be 1 for all the values above 0.

Code;

syms t

[Initializing the symbolic object]

fplot (heaviside (t), [0, 5])

[Using ‘fplot’ function to plot the ‘heaviside’ function with values between 0 and 5]

This is how our input and output will look like in MATLAB:

Input:

example 4

Output:

output 1

As we can see in the output, for the values between 0 and 5, the output is starting from 0.5 (for t = 0), and then it is 1 for all the values above 0.

Example #5

In this example, we will plot the unit step function for values between -5 and 5. As we know, the unit step function gives 0 as output for t < 0, 1 for t > 0 and 0.5 for t = 0, so for the values between -5 and 5, the output will be starting from 0 (for t < 0) and then it will be 0.5 for t = 0 and finally 1 for all the values above 0.

Code:

syms t

[Initializing the symbolic object]

fplot (heaviside (t), [-5, 5])

[Using ‘fplot’ function to plot the ‘heaviside’ function with values between -5 and 5]

This is how our input and output will look like in MATLAB:

Input:

example 5

Output:

output 2

 As we can see in the output, for the values between -5 and 0, the output is 0, and then there is a unit step from 0 to 1 when the input values are in the range of 0 to 5

Conclusion

The unit step function changes from 0 to 1 in almost no time. It can take three values: 0, 1, and ½. It is commonly used to test the low and high-frequency response of any system in a single attempt.

Recommended Articles

This is a guide to Matlab Unit Step Function. Here we discuss the Introduction, syntax, and examples. You may also have a look at the following articles to learn more –

  1.  Nyquist Matlab
  2. Matlab limit
  3. Matlab Saveas
  4. Matlab Cell

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